In his seminal paper on Special Relativity: On the Electrodynamics of Moving Bodies, Einstein derives a formula for the Relativistic Doppler effect. See this section: § 7. Theory of Doppler's Principle and of Aberration The formula is: In this Wiki article, the same formula is derived. The article uses the "the standard Lorentz transformation of the four-momentum". Now here's where it gets a little muddling. Einstein writes: It seems that his formula is a good approximation when we are sufficiently far from the source. However, the four-momentum transformations do not depend on distance, yet they arrive at the exact same formula. What's the reason for this difference?